Modeling the beamfilling correction for microwave retrieval of oceanic rainfall

Beamfilling error refers to the passive microwave rainfall retrieval bias caused by the combined effects of non-uniform distribution of rainfall intensity within the field of view (FOV) of a microwave radiometer and the non-linear relationship between rain rate and microwave brightness temperature over an oceanic background. The beamfilling problem has been studied by many investigators. It is found that even though the beamfilling error for each FOV does vary, the ensemble mean beamfilling error is rather stable and, therefore, can be corrected by a multiplicative constant that depends on the spatial resolution of the observation. This constant is referred to as Beamfilling Correction Factor (BCF).; In previous studies, the beamfilling correction was derived using two-dimensional rainfall intensity fields estimated from radar observations as the basis for simulation studies. Vertical structure and the structure along a sloping radiometer view path have been ignored to date. However, because a radiometer measures the total opacity along its beam as reflected from the ocean surface, and because the absorption coefficient is approximately linear in the rain rate, averaging along the beam does not introduce appreciable error. From the random field theorem, it is known that the variance of a local average is smaller than that of the underlying point process. A reduction in variance will certainly reduce the beamfilling error, suggesting that previous studies have overestimated the beamfilling correction.; A simulation study based on radar observed rainfall data is conducted to estimate the difference between the beamfilling error derived from three-dimensional radar data and that derived from two-dimensional radar data. The three dimensional radar rainfall data used here were collected by the Airborne Rain MApping Radar (ARMAR) during the TOGA-COARE experiment. The ARMAR data have a spatial resolution of less than half of a kilometer which is much better than the 4 km resolution of the radar data collected during GATE. Range sidelobe contamination and signal attenuation through rain associated with ARMAR data are properly treated.; A number of simulations were conducted with different FOV's and for different heights of the 0{dollar}spcirc{dollar}C isotherm (freezing level). The results showed that the beamfilling error is significantly reduced when the three-dimensional rainfall field is used relative to the results when the two-dimensional rainfall field is used for the simulation. Additionally, the results showed that the BCF is logarithmically related to FOV size and linearly related to the freezing level. Finally, a beamfilling correction factor formula that can be used to estimate the BCF for given radiometer parameters (e.g., frequency, polarization, viewing angle, spatial resolution) and freezing level was also derived from these simulation experiments.